2D Orthogonal Grid Generation of Multi-connected Regions Using Modified Finite Point Method
Date Issued
2014
Date
2014
Author(s)
Tsai, Cheng-Yen
Abstract
In this study, the Modified Finite Point Method (MFPM) is used to solve the governing equations which are Laplace equations and to obtain multi-connected region 2-dimensional orthogonal grid.
Modified Finite Point Method (MFPM) is a mesh-less (mesh-free) numerical method. MFPM’s base functions are polynomials and collocate with moving least square(MLS). Compared with Finite Point Method (FPM), collocation of MFPM at boundary takes into account of both governing equations and boundary conditions. It helps to improve the unstable numerical phenomena at boundaries and corners.
Unlike traditional grid-base numerical methods, there is no direct relationship between a point and another nearby point so the boundary conditions are relatively free to be applied. Previously, boundary conditions in traditional numerical methods were restricted to the branch cut so we can only solve certain specific-type grids. Also, it has been found that traditional numerical methods become unstable when solving governing equations directly at the boundary or corners. The MFPM model has been found that with regional connectivity approach it can directly solve the problem stably and obtain orthogonal grids.
In this study, examples using circle, Rankine oval and NACA airfoil as hollowed-out domain are used to generate orthogonal grids. Based on Cauchy-Riemann conditions, Dirichlet’s boundary condition of the internal boundary of hollowed geometry has been derived to improve the accuracy of orthogonal computations.
When hollowed area''s boundary is smooth and no dramatic changes, such as circle, Rankine oval, very stable solutions can be obtained, with very accurate partial derivatives of the solutions. For a very flat Rankine oval, phenomena of numerical instability occurred, especially, near the head and tail of geometry, due to inappropriately including low-related points in different regions into collocation processes. By applying the concept of regional connectivity and dividing the whole domain into sub-domains, accurate collocation only allowed by including grids in appropriate regions. Using this concept, in the case of flat Rankine ovals and NACA airfoils with sharp points, present MFPM performed very well.
Subjects
修正有線配點法
拉普拉斯方程式
柯西里曼條件式
複連通區域
區域連結
無網格數值方法
正交網格
Type
thesis
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